#### The points A (4, -11), B (5, 3), C (2, 15), and D (1, 1) are the vertices of a parallelogram. If the parallelogram is reflected in the y-axis and then in the origin, find the coordinates of the final images. Check whether it remains a parallelogram. Write down a single transformation that brings the above change.

**Solution:**

#### The triangle OAB is reflected in the origin O to triangle OA’B’. A’ and B’ have coordinates (-3, -4) and (0, -5) respectively.

(i) Find the coordinates of A and B.

(ii) Draw a diagram to represent the given information.

(iii) What kind of figure is the quadrilateral ABA’B’?

(iv) Find the coordinates of A”, the reflection of A in the origin followed by reflection in the y-axis.

(v) Find the coordinates of B”, the reflection of B in the x-axis followed by reflection in the origin.

**Solution:**

**More Solutions:**

- Use graph paper for this question.
- AB is a diameter of a circle with centre C (-2, 5).
- The line segment joining A(-1, 5/3) the points B (a, 5).
- In what ratio does the point (5, 4) divide the line segment.
- If A (-4, 3) and B (8, -6), find the length of AB.
- The ratio in which the line segment joining (3, 4) and(-2, 1).